Robert L. Devaney

The book is a useful introduction to a survey of this field of
active research. It is illustrated with many beautiful pictures of
Julia sets, the Mandelbrot set, and other sets related to the
theory.Mathematical Reviews

In the last fifteen years, the Mandelbrot set has emerged as one of
the most recognisable objects in mathematics. While there is no
question of its beauty, relatively few people appreciate
the fact that the mathematics behind such images is equally
beuatiful. This book presents lectures delivered on a wide
range of topics during the AMS Short Course entitled
"Complex Dynamical Systems: The Mathematics Behind the
Mandlebrot and Julia Sets", held at the Joint
Mathematics Meetings in Cincinnati in January 1994. Much of the book
is accessible to anyone with a background in the basics of
dynamical systems and complex analysis.

A.M. Stuart and A.R. Humphries

[Cambridge Monographs on Applied and Computational Mathematics 2]
published by Cambridge University Press

"Essential reading for all those interested in computational dynamical systems ... a
very fine achievement" -- Proc. Edin. Math. Soc.

Dynamical systems are pervasive in the modelling of naturally occurring phenomena. Most of
the models arising in practice cannot be completely solved by analytic techniques; thus,
numerical simulations are of fundamental importance in gaining an understanding of
dynamical systems. It is therefore crucial to understand the behaviour of numerical
simulations of dynamical systems in order to interpret the data obtained from such
simulations and to facilitate the design of algorithms which provide correct qualitative
information without being unduly expensive. These two concerns lead to the study of
the convergence and stability properties of numerical methods for dynamical systems.

The first three chapters of this book contain the elements of the theoryof dynamical
systems and the numerical solution of initial-value problems. In the remaining chapters,
numerical methods are formulated as dynamical systems, and the convergence and stability
properties of the methods are examined. Topics studied include the stability of numerical
methods for contractive, dissipative, gradient, and Hamiltonian systems together with the
convergence properties of equilibria, phase portraits, periodic solutions, and strange
attractors under numerical approximation.

This book will be an invaluable tool for graduate students and researchers in the fields
of numerical analysis and dynamical systems.

T. Kapitaniak

Recently, there has been growing interest among engineers and
applied mathematicians in the potential usefulness of chaotic
behaviour. In this book, new mathematical ideas in nonlinear
dynamics are described so that engineers can apply them in real
physical systems, such as dry friction, chemical reactions,
electronics, and cryptology. The monograph emphasizes mathematical
precision by supplying fundamental definitions and theorems
(but without proofs). Both continuous and discrete dynamical
systems are considered.

R. Sepulchre, M. Jankovic, and P. Kokotovic

Employing passivity as a common thread, this important monograph merges
several streams of nonlinear control to find a constructive solution
of the feedback stabilisation problem. It combines
differential-geometric concepts with the analytic concepts of
passivity, optimality, and Lyapunov stability, so that
geometry may serve as a guide for construction of design
procedures and analysis may provide robustness tools which
geometry lacks. Also includes recursive designs and recursive
Lyapunov designs for feedback, feedforward and interlaced
structures. The book may be used for a first-year
graduate course.

Iosif I. Vorovich

This book presents a mathematically rigorous analysis of the nonlinear
theory of shallow shells. It provides solutions to the general
boundary value problems and gives both analytical and numerical
methods for solving some of the problems in hand. Included are
theorems of existence, results on the stability of solutions,
justification of the numerical methods os solutions, and topological
and variational approaches to the investigations. The new mathematical
results allow for a deeper understanding of the mechanical contents
of the equations of the theory and give a better idea of its possible
applications. The first edition of the book,
entitled Mathematical Problems In the Nonlinear Theory of
Shallow Shells, was published in Russian in 1989. For this
English edition the manuscript has been substantially revised and
expanded.

M. Krstic and H. Deng

This monograph presents the fundamentals of global stabilisation and
optimal control of nonlinear systems with uncertain models.
It offers a unified view of deterministic disturbance attenuation,
stochastic control, and adaptive control for nonlinear systems.
The book addresses a large audience of researchers, students,
engineers and mathematicians in the areas of robust and
adaptive nonlinear control, nonlinear H-infinity stochastic
nonlinear control (including risk-sensitive), and other
related areas of control and dynamical systems theory.

1998 approximately 205pp hardcover
ISBN 1-85233-020-1
Communication and Control Engineering Series